Tag Archives: Disjunctive Syllogisms

Logical Gal and how disjunctive syllogisms help us

16 Oct

Either our government will find a solution for the budget impasse or our country will fall apart.

Our government is working hard to find a solution 

Therefore, it is unlikely that our country will fall apart

Voilà – a proper disjunctive (either/or) syllogism. (Whether it’s true or not, that’s ANOTHER question!)

This way of framing choices is very useful.  Sometimes, however, there are more than 2 options.  And when someone forces you to make a choice, between the two, it is RIGHT to balk and suggest others if they appear to you.

Moms do this frequently, when they are trying to get a child to do something he or she does NOT want to do:

” You can clean your room before going to bed tonight or before going out to play tomorrow morning”

A logical child might say, “Mom, that’s a false dilemma.  How about if I pay my brother to clean my room?  Would that satisfy you?”  Poor Mom!  She had better bone up on logic.

As important as parenting is,  let me direct us to a more serious subject – fear and faith.  The last two days as I’ve been following my Bible reading plan, I’ve come across the same verse in two gospels.  Both Mark 5:36 and Luke 8:50 record Jesus encouraging someone with this logic:  Do not fear, only trust and rely on God. 

The Greek word ‘believe’  or Pisteou (Strong’s 4100)  can be translated this way:  to trust, to believe, to rely on, to put faith in, to entrust, to lean on

The two options are a proper disjunctive – we can either fear circumstances, people, our propensity to make the same mistakes over and over….OR…we can commit our concerns, situations and problems  to God and rely on Him for His help, wisdom, grace, presence, protection and solution.  We can’t do a little of each – simultaneously fearing and trusting. Just think about it:  if we are relying on someone or something, then we are looking to them/it.  And if we are consumed with fear, we are NOT looking at our source of rescue.

Picture a toddler clinging for dear life to MOM.  She is NOT confused about the one she is trusting, clinging to, relying on.

I’ve been helped in a real way these past couple of days as I’ve reminded myself of the fact that there are ONLY TWO CHOICES.  Who wouldn’t want to rely on the God of the Universe who actually promises to supply our needs.  I’m also reminded of God’s  words to us  as spoken through James, half-brother of Jesus, “You have not because you ask not.” 

Using the either/or to argue to a conclusion

5 Aug

“Either you are pro-choice or you are anti-women” 

We ran into this statement as an example of how we need to frame an attribute/predicate as either A or non-A to determine more easily if a pair of statements were truly contradictory.

Framing a contradiction into an either/or hypothetical proposition is one way to argue. We call this a Disjunctive Proposition.

Today we are FIRST going to form a valid or correct argument and then we’ll look at the truth of the major proposition.

Consider the ‘formula’ where P and Q are different statements, called ‘disjuncts’.  On the left is the model syllogism; in the middle and on the right are two samples.

Either P or Q                   Either blue or red            Either she had a boy or a girl

Not  P                               Not blue                             She didn’t have a boy

Therefore, Q                   Tf, red                                 Tf, she had a girl

These arguments work; that is they are valid BECAUSE the major proposition that contains the disjunctive statement tells us that one of the 2 disjuncts is true. (we have to accept this as a given;  we’re NOT going to argue about the truth of that major premise YET.)   So if one disjunct (P or Q) is NOT true, then the other HAS to be true.

What happens, though, if in the 2nd premise, I AFFIRM one of the disjuncts? Can this kind of syllogism work the other way?  It would look like this:

           Either Susie travels to the UK or to France

          Susie travels to France (I’m AFFIRMING one of the 2 disjuncts)

          TF, she does not travel to the UK

No….this set up is INVALID for I have actually assumed MORE than the information given.  It could very well be that her journey takes her to BOTH France and the UK.  All we know from the major premise is that she AT LEAST travels to one of the 2 places.  It does NOT claim that if Susie travels to one, she does NOT then travel to the other.

Certainty exists ONLY if the minor premise (the proposition that denies or affirms one of the disjuncts) denies one of the disjuncts since we have as a given that ONE has to be so.

Either I had a salad for lunch or some soup.

I did not have soup

Tf, I had salad

Back to our original Disjunctive propositions:  Either you are pro-choice or you are anti-women.  Once we have determined that the syllogism is set up correctly, that it is valid, THEN we look at the truth of the major premise.

If you remember what we looked at last Friday, we talked about true dilemmas and the Fallacy of the False Dilemma.  So, is our disjunctive proposition a False Dilemma?

If you are willing, comment with your thoughts about how you would determine the truth or falsity of that proposition.  A lot is riding on your answer!